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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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The Trotter-Kato theorem and approximation of PDEs
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by Kazufumi Ito and Franz Kappel PDF
Math. Comp. 67 (1998), 21-44 Request permission


We present formulations of the Trotter-Kato theorem for approximation of linear C${}_0$-semigroups which provide very useful framework when convergence of numerical approximations to solutions of PDEs are studied. Applicability of our results is demonstrated using a first order hyperbolic equation, a wave equation and Stokes’ equation as illustrative examples.
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Additional Information
  • Kazufumi Ito
  • Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
  • Email:
  • Franz Kappel
  • Affiliation: Institut für Mathematik, Universität Graz, Heinrichstraße 36, A8010 Graz, Austria
  • Email:
  • Received by editor(s): August 18, 1995
  • Received by editor(s) in revised form: August 1, 1996
  • Additional Notes: Research of the first author was supported in part by the NSF under Grant UINT-8521208 and DMS-8818530 and by the Air Force Office of Scientific Research under contract AFOSR-90-0091.
    Research by the second author was supported in part by FWF(Austria) under Grants P6005, P8146-PHY and under F003.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 21-44
  • MSC (1991): Primary 47D05, 47H05, 65J10, 35K22, 35L99
  • DOI:
  • MathSciNet review: 1443120